LMFDB - Embedded newform 1280.2.j.d.63.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1280,2,Mod(63,1280)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1280.63"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1280, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,0,0,0,-32,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.2208514587$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.5
Character	$\chi$	$=$	1280.63
Dual form			1280.2.j.d.447.12

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.81199i q^{3} +(-2.20939 - 0.344369i) q^{5} +(1.54814 - 1.54814i) q^{7} -0.283291 q^{9} +(2.69839 - 2.69839i) q^{11} +3.33474 q^{13} +(-0.623991 + 4.00338i) q^{15} +(-0.680078 + 0.680078i) q^{17} +(2.79866 - 2.79866i) q^{19} +(-2.80521 - 2.80521i) q^{21} +(1.75563 + 1.75563i) q^{23} +(4.76282 + 1.52169i) q^{25} -4.92264i q^{27} +(-3.13750 - 3.13750i) q^{29} +8.56830i q^{31} +(-4.88944 - 4.88944i) q^{33} +(-3.95358 + 2.88732i) q^{35} -8.30361 q^{37} -6.04250i q^{39} -10.8252i q^{41} +2.87092 q^{43} +(0.625900 + 0.0975564i) q^{45} +(-0.985023 - 0.985023i) q^{47} +2.20651i q^{49} +(1.23229 + 1.23229i) q^{51} -13.1354i q^{53} +(-6.89103 + 5.03255i) q^{55} +(-5.07113 - 5.07113i) q^{57} +(4.36188 + 4.36188i) q^{59} +(-7.83616 + 7.83616i) q^{61} +(-0.438574 + 0.438574i) q^{63} +(-7.36775 - 1.14838i) q^{65} -13.0450 q^{67} +(3.18118 - 3.18118i) q^{69} +0.134408 q^{71} +(7.36590 - 7.36590i) q^{73} +(2.75728 - 8.63016i) q^{75} -8.35497i q^{77} +7.88100 q^{79} -9.76962 q^{81} -12.0979i q^{83} +(1.73676 - 1.26836i) q^{85} +(-5.68510 + 5.68510i) q^{87} -15.7833 q^{89} +(5.16265 - 5.16265i) q^{91} +15.5256 q^{93} +(-7.14711 + 5.21957i) q^{95} +(-3.00550 + 3.00550i) q^{97} +(-0.764428 + 0.764428i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{9} + 16 q^{13} + 8 q^{17} + 8 q^{21} + 16 q^{25} - 16 q^{29} + 56 q^{33} - 40 q^{45} - 8 q^{57} - 8 q^{61} - 72 q^{65} + 40 q^{69} + 8 q^{73} - 64 q^{81} - 24 q^{85} - 16 q^{89} + 224 q^{93}+ \cdots + 72 q^{97}+O(q^{100}) $ 32 * q - 32 * q^9 + 16 * q^13 + 8 * q^17 + 8 * q^21 + 16 * q^25 - 16 * q^29 + 56 * q^33 - 40 * q^45 - 8 * q^57 - 8 * q^61 - 72 * q^65 + 40 * q^69 + 8 * q^73 - 64 * q^81 - 24 * q^85 - 16 * q^89 + 224 * q^93 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		−	1.81199i		−	1.04615i	−0.852287	−	0.523075i	$-0.824785\pi$
$3$		−	1.81199i		−	1.04615i	0.852287	−	0.523075i	$-0.175215\pi$
$4$		0			0
$5$	−2.20939	−	0.344369i	−0.988070	−	0.154006i
$5$	−2.20939	−	0.344369i	−0.988070	−	0.154006i
$6$		0			0
$7$	1.54814	−	1.54814i	0.585143	−	0.585143i	−0.351169	−	0.936312i	$-0.614216\pi$
$7$	1.54814	−	1.54814i	0.585143	−	0.585143i	0.936312	+	0.351169i	$0.114216\pi$
$8$		0			0
$9$	−0.283291			−0.0944303
$10$		0			0
$11$	2.69839	−	2.69839i	0.813594	−	0.813594i	−0.171577	−	0.985171i	$-0.554886\pi$
$11$	2.69839	−	2.69839i	0.813594	−	0.813594i	0.985171	+	0.171577i	$0.0548862\pi$
$12$		0			0
$13$	3.33474			0.924890			0.462445	−	0.886648i	$-0.346972\pi$
$13$	3.33474			0.924890			0.462445	+	0.886648i	$0.346972\pi$
$14$		0			0
$15$	−0.623991	+	4.00338i	−0.161114	+	1.03367i
$16$		0			0
$17$	−0.680078	+	0.680078i	−0.164943	+	0.164943i	−0.784752	−	0.619809i	$-0.787210\pi$
$17$	−0.680078	+	0.680078i	−0.164943	+	0.164943i	0.619809	+	0.784752i	$0.287210\pi$
$18$		0			0
$19$	2.79866	−	2.79866i	0.642057	−	0.642057i	−0.309004	−	0.951061i	$-0.599996\pi$
$19$	2.79866	−	2.79866i	0.642057	−	0.642057i	0.951061	+	0.309004i	$0.0999956\pi$
$20$		0			0
$21$	−2.80521	−	2.80521i	−0.612147	−	0.612147i
$22$		0			0
$23$	1.75563	+	1.75563i	0.366074	+	0.366074i	0.866043	−	0.499969i	$-0.166655\pi$
$23$	1.75563	+	1.75563i	0.366074	+	0.366074i	−0.499969	+	0.866043i	$0.666655\pi$
$24$		0			0
$25$	4.76282	+	1.52169i	0.952564	+	0.304338i
$26$		0			0
$27$		−	4.92264i		−	0.947362i
$28$		0			0
$29$	−3.13750	−	3.13750i	−0.582619	−	0.582619i	0.353003	−	0.935622i	$-0.385160\pi$
$29$	−3.13750	−	3.13750i	−0.582619	−	0.582619i	−0.935622	+	0.353003i	$0.885160\pi$
$30$		0			0
$31$			8.56830i			1.53891i	0.638699	+	0.769456i	$0.279473\pi$
$31$			8.56830i			1.53891i	−0.638699	+	0.769456i	$0.720527\pi$
$32$		0			0
$33$	−4.88944	−	4.88944i	−0.851141	−	0.851141i
$34$		0			0
$35$	−3.95358	+	2.88732i	−0.668278	+	0.488046i
$36$		0			0
$37$	−8.30361			−1.36510			−0.682552	−	0.730837i	$-0.739130\pi$
$37$	−8.30361			−1.36510			−0.682552	+	0.730837i	$0.739130\pi$
$38$		0			0
$39$		−	6.04250i		−	0.967574i
$40$		0			0
$41$		−	10.8252i		−	1.69061i	−0.534282	−	0.845306i	$-0.679418\pi$
$41$		−	10.8252i		−	1.69061i	0.534282	−	0.845306i	$-0.320582\pi$
$42$		0			0
$43$	2.87092			0.437811			0.218906	−	0.975746i	$-0.429751\pi$
$43$	2.87092			0.437811			0.218906	+	0.975746i	$0.429751\pi$
$44$		0			0
$45$	0.625900	+	0.0975564i	0.0933037	+	0.0145429i
$46$		0			0
$47$	−0.985023	−	0.985023i	−0.143680	−	0.143680i	0.631608	−	0.775288i	$-0.282395\pi$
$47$	−0.985023	−	0.985023i	−0.143680	−	0.143680i	−0.775288	+	0.631608i	$0.782395\pi$
$48$		0			0
$49$			2.20651i			0.315216i
$50$		0			0
$51$	1.23229	+	1.23229i	0.172555	+	0.172555i
$52$		0			0
$53$		−	13.1354i		−	1.80428i	−0.431441	−	0.902141i	$-0.641995\pi$
$53$		−	13.1354i		−	1.80428i	0.431441	−	0.902141i	$-0.358005\pi$
$54$		0			0
$55$	−6.89103	+	5.03255i	−0.929186	+	0.678589i
$56$		0			0
$57$	−5.07113	−	5.07113i	−0.671688	−	0.671688i
$58$		0			0
$59$	4.36188	+	4.36188i	0.567868	+	0.567868i	0.931531	−	0.363663i	$-0.118474\pi$
$59$	4.36188	+	4.36188i	0.567868	+	0.567868i	−0.363663	+	0.931531i	$0.618474\pi$
$60$		0			0
$61$	−7.83616	+	7.83616i	−1.00332	+	1.00332i	−0.00332328	+	0.999994i	$0.501058\pi$
$61$	−7.83616	+	7.83616i	−1.00332	+	1.00332i	−0.999994	+	0.00332328i	$0.998942\pi$
$62$		0			0
$63$	−0.438574	+	0.438574i	−0.0552552	+	0.0552552i
$64$		0			0
$65$	−7.36775	−	1.14838i	−0.913856	−	0.142439i
$66$		0			0
$67$	−13.0450			−1.59370			−0.796849	−	0.604179i	$-0.793501\pi$
$67$	−13.0450			−1.59370			−0.796849	+	0.604179i	$0.793501\pi$
$68$		0			0
$69$	3.18118	−	3.18118i	0.382968	−	0.382968i
$70$		0			0
$71$	0.134408			0.0159512			0.00797562	−	0.999968i	$-0.497461\pi$
$71$	0.134408			0.0159512			0.00797562	+	0.999968i	$0.497461\pi$
$72$		0			0
$73$	7.36590	−	7.36590i	0.862113	−	0.862113i	−0.129470	−	0.991583i	$-0.541328\pi$
$73$	7.36590	−	7.36590i	0.862113	−	0.862113i	0.991583	+	0.129470i	$0.0413276\pi$
$74$		0			0
$75$	2.75728	−	8.63016i	0.318383	−	0.996525i
$76$		0			0
$77$		−	8.35497i		−	0.952137i
$78$		0			0
$79$	7.88100			0.886682			0.443341	−	0.896353i	$-0.353793\pi$
$79$	7.88100			0.886682			0.443341	+	0.896353i	$0.353793\pi$
$80$		0			0
$81$	−9.76962			−1.08551
$82$		0			0
$83$		−	12.0979i		−	1.32792i	−0.747768	−	0.663961i	$-0.768874\pi$
$83$		−	12.0979i		−	1.32792i	0.747768	−	0.663961i	$-0.231126\pi$
$84$		0			0
$85$	1.73676	−	1.26836i	0.188378	−	0.137573i
$86$		0			0
$87$	−5.68510	+	5.68510i	−0.609507	+	0.609507i
$88$		0			0
$89$	−15.7833			−1.67303			−0.836514	−	0.547945i	$-0.815410\pi$
$89$	−15.7833			−1.67303			−0.836514	+	0.547945i	$0.815410\pi$
$90$		0			0
$91$	5.16265	−	5.16265i	0.541193	−	0.541193i
$92$		0			0
$93$	15.5256			1.60993
$94$		0			0
$95$	−7.14711	+	5.21957i	−0.733278	+	0.535516i
$96$		0			0
$97$	−3.00550	+	3.00550i	−0.305162	+	0.305162i	−0.843029	−	0.537867i	$-0.819230\pi$
$97$	−3.00550	+	3.00550i	−0.305162	+	0.305162i	0.537867	+	0.843029i	$0.319230\pi$
$98$		0			0
$99$	−0.764428	+	0.764428i	−0.0768279	+	0.0768279i
$100$		0			0
$101$	6.84933	+	6.84933i	0.681534	+	0.681534i	0.960346	−	0.278812i	$-0.0899405\pi$
$101$	6.84933	+	6.84933i	0.681534	+	0.681534i	−0.278812	+	0.960346i	$0.589941\pi$
$102$		0			0
$103$	−4.45391	−	4.45391i	−0.438857	−	0.438857i	0.452770	−	0.891627i	$-0.350436\pi$
$103$	−4.45391	−	4.45391i	−0.438857	−	0.438857i	−0.891627	+	0.452770i	$0.850436\pi$
$104$		0			0
$105$	5.23178	+	7.16384i	0.510570	+	0.699119i
$106$		0			0
$107$			14.0189i			1.35526i	0.735403	+	0.677631i	$0.236993\pi$
$107$			14.0189i			1.35526i	−0.735403	+	0.677631i	$0.763007\pi$
$108$		0			0
$109$	7.01357	+	7.01357i	0.671778	+	0.671778i	0.958126	−	0.286348i	$-0.0924413\pi$
$109$	7.01357	+	7.01357i	0.671778	+	0.671778i	−0.286348	+	0.958126i	$0.592441\pi$
$110$		0			0
$111$			15.0460i			1.42810i
$112$		0			0
$113$	7.44675	+	7.44675i	0.700532	+	0.700532i	0.964525	−	0.263993i	$-0.0850395\pi$
$113$	7.44675	+	7.44675i	0.700532	+	0.700532i	−0.263993	+	0.964525i	$0.585040\pi$
$114$		0			0
$115$	−3.27429	−	4.48346i	−0.305329	−	0.418084i
$116$		0			0
$117$	−0.944701			−0.0873376
$118$		0			0
$119$			2.10572i			0.193031i
$120$		0			0
$121$		−	3.56257i		−	0.323870i
$122$		0			0
$123$	−19.6151			−1.76863
$124$		0			0
$125$	−9.99891	−	5.00217i	−0.894330	−	0.447408i
$126$		0			0
$127$	−2.89344	−	2.89344i	−0.256751	−	0.256751i	0.566980	−	0.823732i	$-0.308112\pi$
$127$	−2.89344	−	2.89344i	−0.256751	−	0.256751i	−0.823732	+	0.566980i	$0.808112\pi$
$128$		0			0
$129$		−	5.20206i		−	0.458016i
$130$		0			0
$131$	−0.534493	−	0.534493i	−0.0466989	−	0.0466989i	0.683372	−	0.730071i	$-0.260513\pi$
$131$	−0.534493	−	0.534493i	−0.0466989	−	0.0466989i	−0.730071	+	0.683372i	$0.760513\pi$
$132$		0			0
$133$		−	8.66546i		−	0.751390i
$134$		0			0
$135$	−1.69520	+	10.8760i	−0.145900	+	0.936060i
$136$		0			0
$137$	−4.46199	−	4.46199i	−0.381214	−	0.381214i	0.490326	−	0.871539i	$-0.336878\pi$
$137$	−4.46199	−	4.46199i	−0.381214	−	0.381214i	−0.871539	+	0.490326i	$0.836878\pi$
$138$		0			0
$139$	13.3184	+	13.3184i	1.12965	+	1.12965i	0.990233	+	0.139419i	$0.0445235\pi$
$139$	13.3184	+	13.3184i	1.12965	+	1.12965i	0.139419	+	0.990233i	$0.455476\pi$
$140$		0			0
$141$	−1.78485	+	1.78485i	−0.150311	+	0.150311i
$142$		0			0
$143$	8.99841	−	8.99841i	0.752485	−	0.752485i
$144$		0			0
$145$	5.85150	+	8.01241i	0.485941	+	0.665395i
$146$		0			0
$147$	3.99816			0.329763
$148$		0			0
$149$	−10.3862	+	10.3862i	−0.850874	+	0.850874i	−0.990241	−	0.139366i	$-0.955493\pi$
$149$	−10.3862	+	10.3862i	−0.850874	+	0.850874i	0.139366	+	0.990241i	$0.455493\pi$
$150$		0			0
$151$	6.86253			0.558465			0.279233	−	0.960223i	$-0.409920\pi$
$151$	6.86253			0.558465			0.279233	+	0.960223i	$0.409920\pi$
$152$		0			0
$153$	0.192660	−	0.192660i	0.0155756	−	0.0155756i
$154$		0			0
$155$	2.95065	−	18.9307i	0.237002	−	1.52055i
$156$		0			0
$157$		−	4.58973i		−	0.366300i	−0.983085	−	0.183150i	$-0.941371\pi$
$157$		−	4.58973i		−	0.366300i	0.983085	−	0.183150i	$-0.0586295\pi$
$158$		0			0
$159$	−23.8011			−1.88755
$160$		0			0
$161$	5.43593			0.428411
$162$		0			0
$163$			2.83480i			0.222039i	0.993818	+	0.111019i	$0.0354116\pi$
$163$			2.83480i			0.222039i	−0.993818	+	0.111019i	$0.964588\pi$
$164$		0			0
$165$	9.11891	+	12.4864i	0.709906	+	0.972068i
$166$		0			0
$167$	10.6049	−	10.6049i	0.820629	−	0.820629i	−0.165569	−	0.986198i	$-0.552946\pi$
$167$	10.6049	−	10.6049i	0.820629	−	0.820629i	0.986198	+	0.165569i	$0.0529462\pi$
$168$		0			0
$169$	−1.87951			−0.144578
$170$		0			0
$171$	−0.792835	+	0.792835i	−0.0606296	+	0.0606296i
$172$		0			0
$173$	1.19118			0.0905636			0.0452818	−	0.998974i	$-0.485581\pi$
$173$	1.19118			0.0905636			0.0452818	+	0.998974i	$0.485581\pi$
$174$		0			0
$175$	9.72932	−	5.01773i	0.735467	−	0.379305i
$176$		0			0
$177$	7.90366	−	7.90366i	0.594075	−	0.594075i
$178$		0			0
$179$	3.66019	−	3.66019i	0.273575	−	0.273575i	−0.556962	−	0.830538i	$-0.688033\pi$
$179$	3.66019	−	3.66019i	0.273575	−	0.273575i	0.830538	+	0.556962i	$0.188033\pi$
$180$		0			0
$181$	6.16389	+	6.16389i	0.458158	+	0.458158i	0.898050	−	0.439892i	$-0.144983\pi$
$181$	6.16389	+	6.16389i	0.458158	+	0.458158i	−0.439892	+	0.898050i	$0.644983\pi$
$182$		0			0
$183$	14.1990	+	14.1990i	1.04962	+	1.04962i
$184$		0			0
$185$	18.3459	+	2.85950i	1.34882	+	0.210235i
$186$		0			0
$187$			3.67023i			0.268393i
$188$		0			0
$189$	−7.62094	−	7.62094i	−0.554342	−	0.554342i
$190$		0			0
$191$		−	10.5198i		−	0.761184i	−0.924743	−	0.380592i	$-0.875720\pi$
$191$		−	10.5198i		−	0.761184i	0.924743	−	0.380592i	$-0.124280\pi$
$192$		0			0
$193$	5.63558	+	5.63558i	0.405658	+	0.405658i	0.880221	−	0.474563i	$-0.157394\pi$
$193$	5.63558	+	5.63558i	0.405658	+	0.405658i	−0.474563	+	0.880221i	$0.657394\pi$
$194$		0			0
$195$	−2.08085	+	13.3502i	−0.149013	+	0.956031i
$196$		0			0
$197$	−9.83517			−0.700727			−0.350364	−	0.936614i	$-0.613942\pi$
$197$	−9.83517			−0.700727			−0.350364	+	0.936614i	$0.613942\pi$
$198$		0			0
$199$		−	26.3116i		−	1.86518i	−0.360934	−	0.932592i	$-0.617542\pi$
$199$		−	26.3116i		−	1.86518i	0.360934	−	0.932592i	$-0.382458\pi$
$200$		0			0
$201$			23.6373i			1.66725i
$202$		0			0
$203$	−9.71458			−0.681830
$204$		0			0
$205$	−3.72786	+	23.9171i	−0.260365	+	1.67044i
$206$		0			0
$207$	−0.497354	−	0.497354i	−0.0345685	−	0.0345685i
$208$		0			0
$209$		−	15.1037i		−	1.04475i
$210$		0			0
$211$	18.6349	+	18.6349i	1.28288	+	1.28288i	0.939023	+	0.343853i	$0.111732\pi$
$211$	18.6349	+	18.6349i	1.28288	+	1.28288i	0.343853	+	0.939023i	$0.388268\pi$
$212$		0			0
$213$		−	0.243545i		−	0.0166874i
$214$		0			0
$215$	−6.34298	−	0.988654i	−0.432588	−	0.0674257i
$216$		0			0
$217$	13.2650	+	13.2650i	0.900484	+	0.900484i
$218$		0			0
$219$	−13.3469	−	13.3469i	−0.901900	−	0.901900i
$220$		0			0
$221$	−2.26788	+	2.26788i	−0.152554	+	0.152554i
$222$		0			0
$223$	18.4764	−	18.4764i	1.23727	−	1.23727i	0.276157	−	0.961113i	$-0.410939\pi$
$223$	18.4764	−	18.4764i	1.23727	−	1.23727i	0.961113	−	0.276157i	$-0.0890610\pi$
$224$		0			0
$225$	−1.34926	−	0.431081i	−0.0899509	−	0.0287387i
$226$		0			0
$227$	23.4080			1.55364			0.776821	−	0.629721i	$-0.216831\pi$
$227$	23.4080			1.55364			0.776821	+	0.629721i	$0.216831\pi$
$228$		0			0
$229$	−1.09387	+	1.09387i	−0.0722850	+	0.0722850i	−0.742325	−	0.670040i	$-0.766277\pi$
$229$	−1.09387	+	1.09387i	−0.0722850	+	0.0722850i	0.670040	+	0.742325i	$0.266277\pi$
$230$		0			0
$231$	−15.1391			−0.996079
$232$		0			0
$233$	3.14271	−	3.14271i	0.205886	−	0.205886i	−0.596630	−	0.802516i	$-0.703494\pi$
$233$	3.14271	−	3.14271i	0.205886	−	0.205886i	0.802516	+	0.596630i	$0.203494\pi$
$234$		0			0
$235$	1.83709	+	2.51551i	0.119839	+	0.164094i
$236$		0			0
$237$		−	14.2803i		−	0.927603i
$238$		0			0
$239$	9.46338			0.612135			0.306068	−	0.952010i	$-0.400987\pi$
$239$	9.46338			0.612135			0.306068	+	0.952010i	$0.400987\pi$
$240$		0			0
$241$	5.06898			0.326522			0.163261	−	0.986583i	$-0.447799\pi$
$241$	5.06898			0.326522			0.163261	+	0.986583i	$0.447799\pi$
$242$		0			0
$243$			2.93449i			0.188248i
$244$		0			0
$245$	0.759853	−	4.87504i	0.0485452	−	0.311455i
$246$		0			0
$247$	9.33281	−	9.33281i	0.593832	−	0.593832i
$248$		0			0
$249$	−21.9213			−1.38921
$250$		0			0
$251$	−7.15197	+	7.15197i	−0.451428	+	0.451428i	−0.895828	−	0.444400i	$-0.853417\pi$
$251$	−7.15197	+	7.15197i	−0.451428	+	0.451428i	0.444400	+	0.895828i	$0.353417\pi$
$252$		0			0
$253$	9.47473			0.595671
$254$		0			0
$255$	−2.29825	−	3.14698i	−0.143922	−	0.197071i
$256$		0			0
$257$	4.88244	−	4.88244i	0.304558	−	0.304558i	−0.538236	−	0.842794i	$-0.680909\pi$
$257$	4.88244	−	4.88244i	0.304558	−	0.304558i	0.842794	+	0.538236i	$0.180909\pi$
$258$		0			0
$259$	−12.8552	+	12.8552i	−0.798781	+	0.798781i
$260$		0			0
$261$	0.888824	+	0.888824i	0.0550168	+	0.0550168i
$262$		0			0
$263$	11.9619	+	11.9619i	0.737605	+	0.737605i	0.972114	−	0.234509i	$-0.0753483\pi$
$263$	11.9619	+	11.9619i	0.737605	+	0.737605i	−0.234509	+	0.972114i	$0.575348\pi$
$264$		0			0
$265$	−4.52341	+	29.0212i	−0.277871	+	1.78276i
$266$		0			0
$267$			28.5991i			1.75024i
$268$		0			0
$269$	−12.6832	−	12.6832i	−0.773309	−	0.773309i	0.205375	−	0.978683i	$-0.434159\pi$
$269$	−12.6832	−	12.6832i	−0.773309	−	0.773309i	−0.978683	+	0.205375i	$0.934159\pi$
$270$		0			0
$271$		−	8.14653i		−	0.494867i	−0.968905	−	0.247433i	$-0.920413\pi$
$271$		−	8.14653i		−	0.494867i	0.968905	−	0.247433i	$-0.0795871\pi$
$272$		0			0
$273$	−9.35465	−	9.35465i	−0.566169	−	0.566169i
$274$		0			0
$275$	16.9580	−	8.74582i	1.02261	−	0.527393i
$276$		0			0
$277$	13.5277			0.812800			0.406400	−	0.913695i	$-0.366784\pi$
$277$	13.5277			0.812800			0.406400	+	0.913695i	$0.366784\pi$
$278$		0			0
$279$		−	2.42732i		−	0.145320i
$280$		0			0
$281$			28.4048i			1.69449i	0.531202	+	0.847245i	$0.321741\pi$
$281$			28.4048i			1.69449i	−0.531202	+	0.847245i	$0.678259\pi$
$282$		0			0
$283$	−22.7335			−1.35136			−0.675682	−	0.737193i	$-0.736151\pi$
$283$	−22.7335			−1.35136			−0.675682	+	0.737193i	$0.736151\pi$
$284$		0			0
$285$	9.45778	+	12.9505i	0.560231	+	0.767119i
$286$		0			0
$287$	−16.7590	−	16.7590i	−0.989250	−	0.989250i
$288$		0			0
$289$			16.0750i			0.945588i
$290$		0			0
$291$	5.44592	+	5.44592i	0.319245	+	0.319245i
$292$		0			0
$293$			5.40978i			0.316043i	0.987436	+	0.158021i	$0.0505115\pi$
$293$			5.40978i			0.316043i	−0.987436	+	0.158021i	$0.949489\pi$
$294$		0			0
$295$	−8.13500	−	11.1392i	−0.473638	−	0.648549i
$296$		0			0
$297$	−13.2832	−	13.2832i	−0.770768	−	0.770768i
$298$		0			0
$299$	5.85457	+	5.85457i	0.338578	+	0.338578i
$300$		0			0
$301$	4.44459	−	4.44459i	0.256182	−	0.256182i
$302$		0			0
$303$	12.4109	−	12.4109i	0.712987	−	0.712987i
$304$		0			0
$305$	20.0117	−	14.6146i	1.14587	−	0.836831i
$306$		0			0
$307$	−18.6048			−1.06183			−0.530917	−	0.847424i	$-0.678152\pi$
$307$	−18.6048			−1.06183			−0.530917	+	0.847424i	$0.678152\pi$
$308$		0			0
$309$	−8.07043	+	8.07043i	−0.459111	+	0.459111i
$310$		0			0
$311$	−11.2873			−0.640042			−0.320021	−	0.947410i	$-0.603690\pi$
$311$	−11.2873			−0.640042			−0.320021	+	0.947410i	$0.603690\pi$
$312$		0			0
$313$	23.2411	−	23.2411i	1.31366	−	1.31366i	0.394971	−	0.918694i	$-0.370755\pi$
$313$	23.2411	−	23.2411i	1.31366	−	1.31366i	0.918694	−	0.394971i	$-0.129245\pi$
$314$		0			0
$315$	1.12001	−	0.817951i	0.0631056	−	0.0460863i
$316$		0			0
$317$			3.16629i			0.177837i	0.996039	+	0.0889184i	$0.0283410\pi$
$317$			3.16629i			0.177837i	−0.996039	+	0.0889184i	$0.971659\pi$
$318$		0			0
$319$	−16.9324			−0.948030
$320$		0			0
$321$	25.4021			1.41781
$322$		0			0
$323$			3.80662i			0.211806i
$324$		0			0
$325$	15.8828	+	5.07444i	0.881017	+	0.281479i
$326$		0			0
$327$	12.7085	−	12.7085i	0.702781	−	0.702781i
$328$		0			0
$329$	−3.04991			−0.168147
$330$		0			0
$331$	5.20766	−	5.20766i	0.286239	−	0.286239i	−0.549352	−	0.835591i	$-0.685125\pi$
$331$	5.20766	−	5.20766i	0.286239	−	0.286239i	0.835591	+	0.549352i	$0.185125\pi$
$332$		0			0
$333$	2.35234			0.128907
$334$		0			0
$335$	28.8215	+	4.49228i	1.57468	+	0.245440i
$336$		0			0
$337$	−20.1503	+	20.1503i	−1.09765	+	1.09765i	−0.102970	+	0.994684i	$0.532835\pi$
$337$	−20.1503	+	20.1503i	−1.09765	+	1.09765i	−0.994684	+	0.102970i	$0.967165\pi$
$338$		0			0
$339$	13.4934	−	13.4934i	0.732861	−	0.732861i
$340$		0			0
$341$	23.1206	+	23.1206i	1.25205	+	1.25205i
$342$		0			0
$343$	14.2530	+	14.2530i	0.769589	+	0.769589i
$344$		0			0
$345$	−8.12396	+	5.93296i	−0.437379	+	0.319420i
$346$		0			0
$347$		−	12.9438i		−	0.694861i	−0.937706	−	0.347430i	$-0.887054\pi$
$347$		−	12.9438i		−	0.694861i	0.937706	−	0.347430i	$-0.112946\pi$
$348$		0			0
$349$	0.0888151	+	0.0888151i	0.00475416	+	0.00475416i	0.709480	−	0.704726i	$-0.248930\pi$
$349$	0.0888151	+	0.0888151i	0.00475416	+	0.00475416i	−0.704726	+	0.709480i	$0.748930\pi$
$350$		0			0
$351$		−	16.4157i		−	0.876206i
$352$		0			0
$353$	6.22306	+	6.22306i	0.331220	+	0.331220i	0.853050	−	0.521830i	$-0.174750\pi$
$353$	6.22306	+	6.22306i	0.331220	+	0.331220i	−0.521830	+	0.853050i	$0.674750\pi$
$354$		0			0
$355$	−0.296959	−	0.0462857i	−0.0157609	−	0.00245659i
$356$		0			0
$357$	3.81553			0.201939
$358$		0			0
$359$			22.4574i			1.18525i	0.805477	+	0.592627i	$0.201909\pi$
$359$			22.4574i			1.18525i	−0.805477	+	0.592627i	$0.798091\pi$
$360$		0			0
$361$			3.33498i			0.175525i
$362$		0			0
$363$	−6.45533			−0.338817
$364$		0			0
$365$	−18.8107	+	13.7376i	−0.984599	+	0.719057i
$366$		0			0
$367$	−12.7444	−	12.7444i	−0.665252	−	0.665252i	0.291361	−	0.956613i	$-0.405892\pi$
$367$	−12.7444	−	12.7444i	−0.665252	−	0.665252i	−0.956613	+	0.291361i	$0.905892\pi$
$368$		0			0
$369$			3.06668i			0.159645i
$370$		0			0
$371$	−20.3354	−	20.3354i	−1.05576	−	1.05576i
$372$		0			0
$373$			24.3812i			1.26241i	0.775616	+	0.631205i	$0.217439\pi$
$373$			24.3812i			1.26241i	−0.775616	+	0.631205i	$0.782561\pi$
$374$		0			0
$375$	−9.06387	+	18.1179i	−0.468056	+	0.935603i
$376$		0			0
$377$	−10.4627	−	10.4627i	−0.538858	−	0.538858i
$378$		0			0
$379$	20.9815	+	20.9815i	1.07775	+	1.07775i	0.996711	+	0.0810340i	$0.0258222\pi$
$379$	20.9815	+	20.9815i	1.07775	+	1.07775i	0.0810340	+	0.996711i	$0.474178\pi$
$380$		0			0
$381$	−5.24287	+	5.24287i	−0.268601	+	0.268601i
$382$		0			0
$383$	−13.4514	+	13.4514i	−0.687333	+	0.687333i	−0.961642	−	0.274309i	$-0.911551\pi$
$383$	−13.4514	+	13.4514i	−0.687333	+	0.687333i	0.274309	+	0.961642i	$0.411551\pi$
$384$		0			0
$385$	−2.87719	+	18.4594i	−0.146635	+	0.940778i
$386$		0			0
$387$	−0.813305			−0.0413426
$388$		0			0
$389$	7.64401	−	7.64401i	0.387567	−	0.387567i	−0.486252	−	0.873819i	$-0.661636\pi$
$389$	7.64401	−	7.64401i	0.387567	−	0.387567i	0.873819	+	0.486252i	$0.161636\pi$
$390$		0			0
$391$	−2.38793			−0.120763
$392$		0			0
$393$	−0.968494	+	0.968494i	−0.0488541	+	0.0488541i
$394$		0			0
$395$	−17.4122	−	2.71397i	−0.876104	−	0.136555i
$396$		0			0
$397$			0.575578i			0.0288874i	0.999896	+	0.0144437i	$0.00459774\pi$
$397$			0.575578i			0.0288874i	−0.999896	+	0.0144437i	$0.995402\pi$
$398$		0			0
$399$	−15.7017			−0.786067
$400$		0			0
$401$	−16.7178			−0.834845			−0.417422	−	0.908713i	$-0.637066\pi$
$401$	−16.7178			−0.834845			−0.417422	+	0.908713i	$0.637066\pi$
$402$		0			0
$403$			28.5731i			1.42333i
$404$		0			0
$405$	21.5849	+	3.36435i	1.07256	+	0.167176i
$406$		0			0
$407$	−22.4063	+	22.4063i	−1.11064	+	1.11064i
$408$		0			0
$409$	14.4690			0.715448			0.357724	−	0.933827i	$-0.383553\pi$
$409$	14.4690			0.715448			0.357724	+	0.933827i	$0.383553\pi$
$410$		0			0
$411$	−8.08507	+	8.08507i	−0.398807	+	0.398807i
$412$		0			0
$413$	13.5056			0.664568
$414$		0			0
$415$	−4.16615	+	26.7291i	−0.204508	+	1.31208i
$416$		0			0
$417$	24.1328	−	24.1328i	1.18179	−	1.18179i
$418$		0			0
$419$	−24.5270	+	24.5270i	−1.19822	+	1.19822i	−0.223527	+	0.974698i	$0.571757\pi$
$419$	−24.5270	+	24.5270i	−1.19822	+	1.19822i	−0.974698	+	0.223527i	$0.928243\pi$
$420$		0			0
$421$	−10.6240	−	10.6240i	−0.517783	−	0.517783i	0.399117	−	0.916900i	$-0.369317\pi$
$421$	−10.6240	−	10.6240i	−0.517783	−	0.517783i	−0.916900	+	0.399117i	$0.869317\pi$
$422$		0			0
$423$	0.279048	+	0.279048i	0.0135678	+	0.0135678i
$424$		0			0
$425$	−4.27396	+	2.20422i	−0.207317	+	0.106920i
$426$		0			0
$427$			24.2630i			1.17417i
$428$		0			0
$429$	−16.3050	−	16.3050i	−0.787213	−	0.787213i
$430$		0			0
$431$			2.25550i			0.108644i	0.998523	+	0.0543219i	$0.0172997\pi$
$431$			2.25550i			0.108644i	−0.998523	+	0.0543219i	$0.982700\pi$
$432$		0			0
$433$	19.9639	+	19.9639i	0.959404	+	0.959404i	0.999208	−	0.0398034i	$-0.0126732\pi$
$433$	19.9639	+	19.9639i	0.959404	+	0.959404i	−0.0398034	+	0.999208i	$0.512673\pi$
$434$		0			0
$435$	14.5184	−	10.6028i	0.696103	−	0.508367i
$436$		0			0
$437$	9.82683			0.470081
$438$		0			0
$439$		−	21.0582i		−	1.00505i	−0.864561	−	0.502527i	$-0.832404\pi$
$439$		−	21.0582i		−	1.00505i	0.864561	−	0.502527i	$-0.167596\pi$
$440$		0			0
$441$		−	0.625084i		−	0.0297659i
$442$		0			0
$443$	−19.4033			−0.921877			−0.460938	−	0.887432i	$-0.652487\pi$
$443$	−19.4033			−0.921877			−0.460938	+	0.887432i	$0.652487\pi$
$444$		0			0
$445$	34.8715	+	5.43528i	1.65307	+	0.257657i
$446$		0			0
$447$	18.8197	+	18.8197i	0.890142	+	0.890142i
$448$		0			0
$449$			11.7669i			0.555313i	0.960680	+	0.277656i	$0.0895577\pi$
$449$			11.7669i			0.555313i	−0.960680	+	0.277656i	$0.910442\pi$
$450$		0			0
$451$	−29.2106	−	29.2106i	−1.37547	−	1.37547i
$452$		0			0
$453$		−	12.4348i		−	0.584238i
$454$		0			0
$455$	−13.1842	+	9.62846i	−0.618084	+	0.451389i
$456$		0			0
$457$	−16.1247	−	16.1247i	−0.754280	−	0.754280i	0.220995	−	0.975275i	$-0.429070\pi$
$457$	−16.1247	−	16.1247i	−0.754280	−	0.754280i	−0.975275	+	0.220995i	$0.929070\pi$
$458$		0			0
$459$	3.34778	+	3.34778i	0.156261	+	0.156261i
$460$		0			0
$461$	2.87775	−	2.87775i	0.134030	−	0.134030i	−0.636909	−	0.770939i	$-0.719787\pi$
$461$	2.87775	−	2.87775i	0.134030	−	0.134030i	0.770939	+	0.636909i	$0.219787\pi$
$462$		0			0
$463$	−9.81984	+	9.81984i	−0.456367	+	0.456367i	−0.897461	−	0.441094i	$-0.854590\pi$
$463$	−9.81984	+	9.81984i	−0.456367	+	0.456367i	0.441094	+	0.897461i	$0.354590\pi$
$464$		0			0
$465$	−34.3022	−	5.34654i	−1.59073	−	0.247940i
$466$		0			0
$467$	21.7864			1.00816			0.504078	−	0.863658i	$-0.331832\pi$
$467$	21.7864			1.00816			0.504078	+	0.863658i	$0.331832\pi$
$468$		0			0
$469$	−20.1955	+	20.1955i	−0.932541	+	0.932541i
$470$		0			0
$471$	−8.31652			−0.383205
$472$		0			0
$473$	7.74685	−	7.74685i	0.356200	−	0.356200i
$474$		0			0
$475$	17.5882	−	9.07083i	0.807003	−	0.416198i
$476$		0			0
$477$			3.72113i			0.170379i
$478$		0			0
$479$	9.22756			0.421618			0.210809	−	0.977527i	$-0.432390\pi$
$479$	9.22756			0.421618			0.210809	+	0.977527i	$0.432390\pi$
$480$		0			0
$481$	−27.6904			−1.26257
$482$		0			0
$483$		−	9.84982i		−	0.448183i
$484$		0			0
$485$	7.67532	−	5.60532i	0.348518	−	0.254525i
$486$		0			0
$487$	25.1713	−	25.1713i	1.14062	−	1.14062i	0.152284	−	0.988337i	$-0.451337\pi$
$487$	25.1713	−	25.1713i	1.14062	−	1.14062i	0.988337	−	0.152284i	$-0.0486628\pi$
$488$		0			0
$489$	5.13662			0.232286
$490$		0			0
$491$	20.1548	−	20.1548i	0.909574	−	0.909574i	−0.0866633	−	0.996238i	$-0.527620\pi$
$491$	20.1548	−	20.1548i	0.909574	−	0.909574i	0.996238	+	0.0866633i	$0.0276204\pi$
$492$		0			0
$493$	4.26749			0.192198
$494$		0			0
$495$	1.95217	−	1.42568i	0.0877433	−	0.0640793i
$496$		0			0
$497$	0.208082	−	0.208082i	0.00933376	−	0.00933376i
$498$		0			0
$499$	−3.44858	+	3.44858i	−0.154380	+	0.154380i	−0.780071	−	0.625691i	$-0.784817\pi$
$499$	−3.44858	+	3.44858i	−0.154380	+	0.154380i	0.625691	+	0.780071i	$0.284817\pi$
$500$		0			0
$501$	−19.2159	−	19.2159i	−0.858501	−	0.858501i
$502$		0			0
$503$	14.8039	+	14.8039i	0.660074	+	0.660074i	0.955397	−	0.295323i	$-0.0954274\pi$
$503$	14.8039	+	14.8039i	0.660074	+	0.660074i	−0.295323	+	0.955397i	$0.595427\pi$
$504$		0			0
$505$	−12.7742	−	17.4916i	−0.568443	−	0.778364i
$506$		0			0
$507$			3.40564i			0.151250i
$508$		0			0
$509$	−14.7467	−	14.7467i	−0.653635	−	0.653635i	0.300232	−	0.953866i	$-0.402936\pi$
$509$	−14.7467	−	14.7467i	−0.653635	−	0.653635i	−0.953866	+	0.300232i	$0.902936\pi$
$510$		0			0
$511$		−	22.8069i		−	1.00892i
$512$		0			0
$513$	−13.7768	−	13.7768i	−0.608261	−	0.608261i
$514$		0			0
$515$	8.30665	+	11.3742i	0.366035	+	0.501208i
$516$		0			0
$517$	−5.31594			−0.233795
$518$		0			0
$519$		−	2.15840i		−	0.0947431i
$520$		0			0
$521$			15.2957i			0.670118i	0.942197	+	0.335059i	$0.108756\pi$
$521$			15.2957i			0.670118i	−0.942197	+	0.335059i	$0.891244\pi$
$522$		0			0
$523$	−0.856013			−0.0374308			−0.0187154	−	0.999825i	$-0.505958\pi$
$523$	−0.856013			−0.0374308			−0.0187154	+	0.999825i	$0.505958\pi$
$524$		0			0
$525$	−9.09206	−	17.6294i	−0.396810	−	0.769409i
$526$		0			0
$527$	−5.82712	−	5.82712i	−0.253833	−	0.253833i
$528$		0			0
$529$		−	16.8355i		−	0.731980i
$530$		0			0
$531$	−1.23568	−	1.23568i	−0.0536239	−	0.0536239i
$532$		0			0
$533$		−	36.0992i		−	1.56363i
$534$		0			0
$535$	4.82768	−	30.9733i	0.208719	−	1.33909i
$536$		0			0
$537$	−6.63221	−	6.63221i	−0.286201	−	0.286201i
$538$		0			0
$539$	5.95402	+	5.95402i	0.256458	+	0.256458i
$540$		0			0
$541$	−3.59516	+	3.59516i	−0.154568	+	0.154568i	−0.780155	−	0.625587i	$-0.784860\pi$
$541$	−3.59516	+	3.59516i	−0.154568	+	0.154568i	0.625587	+	0.780155i	$0.284860\pi$
$542$		0			0
$543$	11.1689	−	11.1689i	0.479302	−	0.479302i
$544$		0			0
$545$	−13.0805	−	17.9110i	−0.560306	−	0.767222i
$546$		0			0
$547$	−2.45850			−0.105118			−0.0525589	−	0.998618i	$-0.516738\pi$
$547$	−2.45850			−0.105118			−0.0525589	+	0.998618i	$0.516738\pi$
$548$		0			0
$549$	2.21991	−	2.21991i	0.0947436	−	0.0947436i
$550$		0			0
$551$	−17.5616			−0.748149
$552$		0			0
$553$	12.2009	−	12.2009i	0.518836	−	0.518836i
$554$		0			0
$555$	5.18137	−	33.2425i	0.219937	−	1.41107i
$556$		0			0
$557$			13.9664i			0.591774i	0.955223	+	0.295887i	$0.0956152\pi$
$557$			13.9664i			0.591774i	−0.955223	+	0.295887i	$0.904385\pi$
$558$		0			0
$559$	9.57377			0.404927
$560$		0			0
$561$	6.65039			0.280780
$562$		0			0
$563$		−	3.68729i		−	0.155401i	−0.996977	−	0.0777004i	$-0.975242\pi$
$563$		−	3.68729i		−	0.155401i	0.996977	−	0.0777004i	$-0.0247578\pi$
$564$		0			0
$565$	−13.8884	−	19.0172i	−0.584288	−	0.800061i
$566$		0			0
$567$	−15.1248	+	15.1248i	−0.635180	+	0.635180i
$568$		0			0
$569$	2.38759			0.100093			0.0500466	−	0.998747i	$-0.484063\pi$
$569$	2.38759			0.100093			0.0500466	+	0.998747i	$0.484063\pi$
$570$		0			0
$571$	12.9632	−	12.9632i	0.542491	−	0.542491i	−0.381767	−	0.924258i	$-0.624684\pi$
$571$	12.9632	−	12.9632i	0.542491	−	0.542491i	0.924258	+	0.381767i	$0.124684\pi$
$572$		0			0
$573$	−19.0617			−0.796313
$574$		0			0
$575$	5.69023	+	11.0333i	0.237299	+	0.460119i
$576$		0			0
$577$	4.15876	−	4.15876i	0.173131	−	0.173131i	−0.615222	−	0.788354i	$-0.710934\pi$
$577$	4.15876	−	4.15876i	0.173131	−	0.173131i	0.788354	+	0.615222i	$0.210934\pi$
$578$		0			0
$579$	10.2116	−	10.2116i	0.424379	−	0.424379i
$580$		0			0
$581$	−18.7293	−	18.7293i	−0.777024	−	0.777024i
$582$		0			0
$583$	−35.4443	−	35.4443i	−1.46795	−	1.46795i
$584$		0			0
$585$	2.08721	+	0.325325i	0.0862957	+	0.0134505i
$586$		0			0
$587$		−	33.0229i		−	1.36300i	−0.731818	−	0.681500i	$-0.761328\pi$
$587$		−	33.0229i		−	1.36300i	0.731818	−	0.681500i	$-0.238672\pi$
$588$		0			0
$589$	23.9798	+	23.9798i	0.988070	+	0.988070i
$590$		0			0
$591$			17.8212i			0.733066i
$592$		0			0
$593$	−11.3559	−	11.3559i	−0.466330	−	0.466330i	0.434394	−	0.900723i	$-0.356963\pi$
$593$	−11.3559	−	11.3559i	−0.466330	−	0.466330i	−0.900723	+	0.434394i	$0.856963\pi$
$594$		0			0
$595$	0.725142	−	4.65235i	0.0297279	−	0.190728i
$596$		0			0
$597$	−47.6763			−1.95126
$598$		0			0
$599$			15.5317i			0.634607i	0.948324	+	0.317304i	$0.102777\pi$
$599$			15.5317i			0.634607i	−0.948324	+	0.317304i	$0.897223\pi$
$600$		0			0
$601$			23.2823i			0.949705i	0.880065	+	0.474853i	$0.157499\pi$
$601$			23.2823i			0.949705i	−0.880065	+	0.474853i	$0.842501\pi$
$602$		0			0
$603$	3.69552			0.150493
$604$		0			0
$605$	−1.22684	+	7.87111i	−0.0498780	+	0.320006i
$606$		0			0
$607$	23.0138	+	23.0138i	0.934099	+	0.934099i	0.997959	−	0.0638595i	$-0.0203410\pi$
$607$	23.0138	+	23.0138i	0.934099	+	0.934099i	−0.0638595	+	0.997959i	$0.520341\pi$
$608$		0			0
$609$			17.6027i			0.713297i
$610$		0			0
$611$	−3.28480	−	3.28480i	−0.132889	−	0.132889i
$612$		0			0
$613$		−	23.8396i		−	0.962874i	−0.876481	−	0.481437i	$-0.840115\pi$
$613$		−	23.8396i		−	0.962874i	0.876481	−	0.481437i	$-0.159885\pi$
$614$		0			0
$615$	43.3375	+	6.75483i	1.74753	+	0.272381i
$616$		0			0
$617$	−7.51162	−	7.51162i	−0.302406	−	0.302406i	0.539548	−	0.841955i	$-0.318595\pi$
$617$	−7.51162	−	7.51162i	−0.302406	−	0.302406i	−0.841955	+	0.539548i	$0.818595\pi$
$618$		0			0
$619$	3.21702	+	3.21702i	0.129303	+	0.129303i	0.768796	−	0.639494i	$-0.220856\pi$
$619$	3.21702	+	3.21702i	0.129303	+	0.129303i	−0.639494	+	0.768796i	$0.720856\pi$
$620$		0			0
$621$	8.64233	−	8.64233i	0.346805	−	0.346805i
$622$		0			0
$623$	−24.4348	+	24.4348i	−0.978961	+	0.978961i
$624$		0			0
$625$	20.3689	+	14.4951i	0.814757	+	0.579803i
$626$		0			0
$627$	−27.3678			−1.09296
$628$		0			0
$629$	5.64710	−	5.64710i	0.225165	−	0.225165i
$630$		0			0
$631$	17.5142			0.697231			0.348616	−	0.937266i	$-0.386652\pi$
$631$	17.5142			0.697231			0.348616	+	0.937266i	$0.386652\pi$
$632$		0			0
$633$	33.7661	−	33.7661i	1.34208	−	1.34208i
$634$		0			0
$635$	5.39634	+	7.38916i	0.214147	+	0.293230i
$636$		0			0
$637$			7.35814i			0.291540i
$638$		0			0
$639$	−0.0380764			−0.00150628
$640$		0			0
$641$	−4.81236			−0.190077			−0.0950383	−	0.995474i	$-0.530297\pi$
$641$	−4.81236			−0.190077			−0.0950383	+	0.995474i	$0.530297\pi$
$642$		0			0
$643$			0.379678i			0.0149730i	0.999972	+	0.00748652i	$0.00238306\pi$
$643$			0.379678i			0.0149730i	−0.999972	+	0.00748652i	$0.997617\pi$
$644$		0			0
$645$	−1.79143	+	11.4934i	−0.0705374	+	0.452552i
$646$		0			0
$647$	10.4814	−	10.4814i	0.412066	−	0.412066i	−0.470392	−	0.882458i	$-0.655887\pi$
$647$	10.4814	−	10.4814i	0.412066	−	0.412066i	0.882458	+	0.470392i	$0.155887\pi$
$648$		0			0
$649$	23.5401			0.924028
$650$		0			0
$651$	24.0359	−	24.0359i	0.942041	−	0.942041i
$652$		0			0
$653$	−3.39325			−0.132788			−0.0663941	−	0.997793i	$-0.521149\pi$
$653$	−3.39325			−0.132788			−0.0663941	+	0.997793i	$0.521149\pi$
$654$		0			0
$655$	0.996843	+	1.36497i	0.0389499	+	0.0533337i
$656$		0			0
$657$	−2.08669	+	2.08669i	−0.0814096	+	0.0814096i
$658$		0			0
$659$	3.63069	−	3.63069i	0.141431	−	0.141431i	−0.632846	−	0.774278i	$-0.718113\pi$
$659$	3.63069	−	3.63069i	0.141431	−	0.141431i	0.774278	+	0.632846i	$0.218113\pi$
$660$		0			0
$661$	−7.92705	−	7.92705i	−0.308327	−	0.308327i	0.535934	−	0.844260i	$-0.319960\pi$
$661$	−7.92705	−	7.92705i	−0.308327	−	0.308327i	−0.844260	+	0.535934i	$0.819960\pi$
$662$		0			0
$663$	4.10937	+	4.10937i	0.159595	+	0.159595i
$664$		0			0
$665$	−2.98411	+	19.1454i	−0.115719	+	0.742426i
$666$		0			0
$667$		−	11.0166i		−	0.426563i
$668$		0			0
$669$	−33.4789	−	33.4789i	−1.29437	−	1.29437i
$670$		0			0
$671$			42.2900i			1.63259i
$672$		0			0
$673$	−6.74727	−	6.74727i	−0.260088	−	0.260088i	0.565002	−	0.825090i	$-0.308876\pi$
$673$	−6.74727	−	6.74727i	−0.260088	−	0.260088i	−0.825090	+	0.565002i	$0.808876\pi$
$674$		0			0
$675$	7.49073	−	23.4456i	0.288318	−	0.902423i
$676$		0			0
$677$	−21.3785			−0.821641			−0.410821	−	0.911716i	$-0.634758\pi$
$677$	−21.3785			−0.821641			−0.410821	+	0.911716i	$0.634758\pi$
$678$		0			0
$679$			9.30588i			0.357127i
$680$		0			0
$681$		−	42.4149i		−	1.62534i
$682$		0			0
$683$	14.6001			0.558658			0.279329	−	0.960195i	$-0.409888\pi$
$683$	14.6001			0.558658			0.279329	+	0.960195i	$0.409888\pi$
$684$		0			0
$685$	8.32172	+	11.3949i	0.317957	+	0.435375i
$686$		0			0
$687$	1.98208	+	1.98208i	0.0756210	+	0.0756210i
$688$		0			0
$689$		−	43.8031i		−	1.66876i
$690$		0			0
$691$	21.0583	+	21.0583i	0.801097	+	0.801097i	0.983267	−	0.182170i	$-0.0583121\pi$
$691$	21.0583	+	21.0583i	0.801097	+	0.801097i	−0.182170	+	0.983267i	$0.558312\pi$
$692$		0			0
$693$			2.36689i			0.0899106i
$694$		0			0
$695$	−24.8391	−	34.0120i	−0.942202	−	1.29015i
$696$		0			0
$697$	7.36198	+	7.36198i	0.278855	+	0.278855i
$698$		0			0
$699$	−5.69455	−	5.69455i	−0.215388	−	0.215388i
$700$		0			0
$701$	27.3282	−	27.3282i	1.03217	−	1.03217i	0.0327069	−	0.999465i	$-0.489587\pi$
$701$	27.3282	−	27.3282i	1.03217	−	1.03217i	0.999465	−	0.0327069i	$-0.0104128\pi$
$702$		0			0
$703$	−23.2390	+	23.2390i	−0.876475	+	0.876475i
$704$		0			0
$705$	4.55807	−	3.32878i	0.171667	−	0.125369i
$706$		0			0
$707$	21.2075			0.797590
$708$		0			0
$709$	−28.3895	+	28.3895i	−1.06619	+	1.06619i	−0.0685403	+	0.997648i	$0.521834\pi$
$709$	−28.3895	+	28.3895i	−1.06619	+	1.06619i	−0.997648	+	0.0685403i	$0.978166\pi$
$710$		0			0
$711$	−2.23262			−0.0837296
$712$		0			0
$713$	−15.0428	+	15.0428i	−0.563356	+	0.563356i
$714$		0			0
$715$	−22.9798	+	16.7822i	−0.859395	+	0.627621i
$716$		0			0
$717$		−	17.1475i		−	0.640385i
$718$		0			0
$719$	−22.2952			−0.831471			−0.415736	−	0.909486i	$-0.636476\pi$
$719$	−22.2952			−0.831471			−0.415736	+	0.909486i	$0.636476\pi$
$720$		0			0
$721$	−13.7906			−0.513588
$722$		0			0
$723$		−	9.18491i		−	0.341591i
$724$		0			0
$725$	−10.1690	−	19.7176i	−0.377669	−	0.732295i
$726$		0			0
$727$	20.3177	−	20.3177i	0.753543	−	0.753543i	−0.221596	−	0.975139i	$-0.571127\pi$
$727$	20.3177	−	20.3177i	0.753543	−	0.753543i	0.975139	+	0.221596i	$0.0711265\pi$
$728$		0			0
$729$	−23.9916			−0.888578
$730$		0			0
$731$	−1.95245	+	1.95245i	−0.0722139	+	0.0722139i
$732$		0			0
$733$	1.80400			0.0666323			0.0333162	−	0.999445i	$-0.489393\pi$
$733$	1.80400			0.0666323			0.0333162	+	0.999445i	$0.489393\pi$
$734$		0			0
$735$	−8.83351	−	1.37684i	−0.325829	−	0.0507856i
$736$		0			0
$737$	−35.2004	+	35.2004i	−1.29662	+	1.29662i
$738$		0			0
$739$	−0.240927	+	0.240927i	−0.00886264	+	0.00886264i	−0.711524	−	0.702662i	$-0.751995\pi$
$739$	−0.240927	+	0.240927i	−0.00886264	+	0.00886264i	0.702662	+	0.711524i	$0.251995\pi$
$740$		0			0
$741$	−16.9109	−	16.9109i	−0.621238	−	0.621238i
$742$		0			0
$743$	35.9128	+	35.9128i	1.31751	+	1.31751i	0.915738	+	0.401775i	$0.131607\pi$
$743$	35.9128	+	35.9128i	1.31751	+	1.31751i	0.401775	+	0.915738i	$0.368393\pi$
$744$		0			0
$745$	26.5240	−	19.3706i	0.971763	−	0.709683i
$746$		0			0
$747$			3.42723i			0.125396i
$748$		0			0
$749$	21.7033	+	21.7033i	0.793021	+	0.793021i
$750$		0			0
$751$			22.2372i			0.811448i	0.913996	+	0.405724i	$0.132981\pi$
$751$			22.2372i			0.811448i	−0.913996	+	0.405724i	$0.867019\pi$
$752$		0			0
$753$	12.9593	+	12.9593i	0.472262	+	0.472262i
$754$		0			0
$755$	−15.1620	−	2.36324i	−0.551803	−	0.0860072i
$756$		0			0
$757$	8.65429			0.314545			0.157273	−	0.987555i	$-0.449730\pi$
$757$	8.65429			0.314545			0.157273	+	0.987555i	$0.449730\pi$
$758$		0			0
$759$		−	17.1681i		−	0.623162i
$760$		0			0
$761$		−	51.2052i		−	1.85619i	−0.372345	−	0.928094i	$-0.621446\pi$
$761$		−	51.2052i		−	1.85619i	0.372345	−	0.928094i	$-0.378554\pi$
$762$		0			0
$763$	21.7160			0.786172
$764$		0			0
$765$	−0.492007	+	0.359315i	−0.0177885	+	0.0129911i
$766$		0			0
$767$	14.5457	+	14.5457i	0.525216	+	0.525216i
$768$		0			0
$769$			6.33900i			0.228590i	0.993447	+	0.114295i	$0.0364610\pi$
$769$			6.33900i			0.228590i	−0.993447	+	0.114295i	$0.963539\pi$
$770$		0			0
$771$	−8.84691	−	8.84691i	−0.318614	−	0.318614i
$772$		0			0
$773$			49.9518i			1.79664i	0.439341	+	0.898321i	$0.355212\pi$
$773$			49.9518i			1.79664i	−0.439341	+	0.898321i	$0.644788\pi$
$774$		0			0
$775$	−13.0383	+	40.8093i	−0.468350	+	1.46591i
$776$		0			0
$777$	23.2934	+	23.2934i	0.835645	+	0.835645i
$778$		0			0
$779$	−30.2961	−	30.2961i	−1.08547	−	1.08547i
$780$		0			0
$781$	0.362683	−	0.362683i	0.0129778	−	0.0129778i
$782$		0			0
$783$	−15.4448	+	15.4448i	−0.551951	+	0.551951i
$784$		0			0
$785$	−1.58056	+	10.1405i	−0.0564126	+	0.361930i
$786$		0			0
$787$	−41.6365			−1.48418			−0.742090	−	0.670300i	$-0.766165\pi$
$787$	−41.6365			−1.48418			−0.742090	+	0.670300i	$0.766165\pi$
$788$		0			0
$789$	21.6749	−	21.6749i	0.771645	−	0.771645i
$790$		0			0
$791$	23.0573			0.819822
$792$		0			0
$793$	−26.1316	+	26.1316i	−0.927959	+	0.927959i
$794$		0			0
$795$	52.5860	+	8.19635i	1.86503	+	0.290695i
$796$		0			0
$797$		−	29.3268i		−	1.03881i	−0.854528	−	0.519405i	$-0.826154\pi$
$797$		−	29.3268i		−	1.03881i	0.854528	−	0.519405i	$-0.173846\pi$
$798$		0			0
$799$	1.33978			0.0473982
$800$		0			0
$801$	4.47127			0.157984
$802$		0			0
$803$		−	39.7521i		−	1.40282i
$804$		0			0
$805$	−12.0101	−	1.87196i	−0.423300	−	0.0659780i
$806$		0			0
$807$	−22.9818	+	22.9818i	−0.808997	+	0.808997i
$808$		0			0
$809$	−6.43307			−0.226175			−0.113087	−	0.993585i	$-0.536074\pi$
$809$	−6.43307			−0.226175			−0.113087	+	0.993585i	$0.536074\pi$
$810$		0			0
$811$	−14.4038	+	14.4038i	−0.505786	+	0.505786i	−0.913230	−	0.407444i	$-0.866420\pi$
$811$	−14.4038	+	14.4038i	−0.505786	+	0.505786i	0.407444	+	0.913230i	$0.366420\pi$
$812$		0			0
$813$	−14.7614			−0.517705
$814$		0			0
$815$	0.976217	−	6.26319i	0.0341954	−	0.219390i
$816$		0			0
$817$	8.03473	−	8.03473i	0.281100	−	0.281100i
$818$		0			0
$819$	−1.46253	+	1.46253i	−0.0511050	+	0.0511050i
$820$		0			0
$821$	20.5284	+	20.5284i	0.716446	+	0.716446i	0.967876	−	0.251429i	$-0.0809006\pi$
$821$	20.5284	+	20.5284i	0.716446	+	0.716446i	−0.251429	+	0.967876i	$0.580901\pi$
$822$		0			0
$823$	−13.8988	−	13.8988i	−0.484481	−	0.484481i	0.422078	−	0.906559i	$-0.361301\pi$
$823$	−13.8988	−	13.8988i	−0.484481	−	0.484481i	−0.906559	+	0.422078i	$0.861301\pi$
$824$		0			0
$825$	−15.8473	−	30.7277i	−0.551732	−	1.06980i
$826$		0			0
$827$		−	29.3843i		−	1.02179i	−0.859642	−	0.510897i	$-0.829313\pi$
$827$		−	29.3843i		−	1.02179i	0.859642	−	0.510897i	$-0.170687\pi$
$828$		0			0
$829$	34.7193	+	34.7193i	1.20585	+	1.20585i	0.972359	+	0.233492i	$0.0750154\pi$
$829$	34.7193	+	34.7193i	1.20585	+	1.20585i	0.233492	+	0.972359i	$0.424985\pi$
$830$		0			0
$831$		−	24.5120i		−	0.850310i
$832$		0			0
$833$	−1.50060	−	1.50060i	−0.0519927	−	0.0519927i
$834$		0			0
$835$	−27.0823	+	19.7783i	−0.937220	+	0.684457i
$836$		0			0
$837$	42.1787			1.45791
$838$		0			0
$839$			4.78293i			0.165125i	0.996586	+	0.0825626i	$0.0263104\pi$
$839$			4.78293i			0.165125i	−0.996586	+	0.0825626i	$0.973690\pi$
$840$		0			0
$841$		−	9.31222i		−	0.321111i
$842$		0			0
$843$	51.4692			1.77269
$844$		0			0
$845$	4.15257	+	0.647244i	0.142853	+	0.0222659i
$846$		0			0
$847$	−5.51537	−	5.51537i	−0.189510	−	0.189510i
$848$		0			0
$849$			41.1927i			1.41373i
$850$		0			0
$851$	−14.5781	−	14.5781i	−0.499729	−	0.499729i
$852$		0			0
$853$		−	45.2839i		−	1.55049i	−0.631659	−	0.775246i	$-0.717626\pi$
$853$		−	45.2839i		−	1.55049i	0.631659	−	0.775246i	$-0.282374\pi$
$854$		0			0
$855$	2.02471	−	1.47866i	0.0692436	−	0.0505690i
$856$		0			0
$857$	2.73476	+	2.73476i	0.0934175	+	0.0934175i	0.752271	−	0.658854i	$-0.228958\pi$
$857$	2.73476	+	2.73476i	0.0934175	+	0.0934175i	−0.658854	+	0.752271i	$0.728958\pi$
$858$		0			0
$859$	5.94695	+	5.94695i	0.202907	+	0.202907i	0.801244	−	0.598337i	$-0.204172\pi$
$859$	5.94695	+	5.94695i	0.202907	+	0.202907i	−0.598337	+	0.801244i	$0.704172\pi$
$860$		0			0
$861$	−30.3670	+	30.3670i	−1.03490	+	1.03490i
$862$		0			0
$863$	34.3328	−	34.3328i	1.16870	−	1.16870i	0.186187	−	0.982514i	$-0.440387\pi$
$863$	34.3328	−	34.3328i	1.16870	−	1.16870i	0.982514	−	0.186187i	$-0.0596130\pi$
$864$		0			0
$865$	−2.63178	−	0.410204i	−0.0894832	−	0.0139474i
$866$		0			0
$867$	29.1276			0.989227
$868$		0			0
$869$	21.2660	−	21.2660i	0.721399	−	0.721399i
$870$		0			0
$871$	−43.5016			−1.47400
$872$		0			0
$873$	0.851430	−	0.851430i	0.0288165	−	0.0288165i
$874$		0			0
$875$	−23.2238	+	7.73566i	−0.785108	+	0.261513i
$876$		0			0
$877$			3.27398i			0.110555i	0.998471	+	0.0552773i	$0.0176043\pi$
$877$			3.27398i			0.110555i	−0.998471	+	0.0552773i	$0.982396\pi$
$878$		0			0
$879$	9.80244			0.330628
$880$		0			0
$881$	39.5807			1.33351			0.666753	−	0.745279i	$-0.267684\pi$
$881$	39.5807			1.33351			0.666753	+	0.745279i	$0.267684\pi$
$882$		0			0
$883$			17.8181i			0.599628i	0.953998	+	0.299814i	$0.0969246\pi$
$883$			17.8181i			0.599628i	−0.953998	+	0.299814i	$0.903075\pi$
$884$		0			0
$885$	−20.1841	+	14.7405i	−0.678479	+	0.495497i
$886$		0			0
$887$	−20.2924	+	20.2924i	−0.681352	+	0.681352i	−0.960305	−	0.278953i	$-0.910013\pi$
$887$	−20.2924	+	20.2924i	−0.681352	+	0.681352i	0.278953	+	0.960305i	$0.410013\pi$
$888$		0			0
$889$	−8.95892			−0.300473
$890$		0			0
$891$	−26.3622	+	26.3622i	−0.883167	+	0.883167i
$892$		0			0
$893$	−5.51349			−0.184502
$894$		0			0
$895$	−9.34724	+	6.82633i	−0.312444	+	0.228179i
$896$		0			0
$897$	10.6084	−	10.6084i	0.354204	−	0.354204i
$898$		0			0
$899$	26.8830	−	26.8830i	0.896599	−	0.896599i
$900$		0			0
$901$	8.93308	+	8.93308i	0.297604	+	0.297604i
$902$		0			0
$903$	−8.05354	−	8.05354i	−0.268005	−	0.268005i
$904$		0			0
$905$	−11.4958	−	15.7411i	−0.382133	−	0.523251i
$906$		0			0
$907$			31.2744i			1.03845i	0.854638	+	0.519225i	$0.173779\pi$
$907$			31.2744i			1.03845i	−0.854638	+	0.519225i	$0.826221\pi$
$908$		0			0
$909$	−1.94035	−	1.94035i	−0.0643574	−	0.0643574i
$910$		0			0
$911$			16.8051i			0.556777i	0.960469	+	0.278388i	$0.0898002\pi$
$911$			16.8051i			0.556777i	−0.960469	+	0.278388i	$0.910200\pi$
$912$		0			0
$913$	−32.6449	−	32.6449i	−1.08039	−	1.08039i
$914$		0			0
$915$	−26.4815	−	36.2609i	−0.875451	−	1.19875i
$916$		0			0
$917$	−1.65494			−0.0546511
$918$		0			0
$919$		−	6.78337i		−	0.223763i	−0.993722	−	0.111881i	$-0.964312\pi$
$919$		−	6.78337i		−	0.223763i	0.993722	−	0.111881i	$-0.0356876\pi$
$920$		0			0
$921$			33.7117i			1.11084i
$922$		0			0
$923$	0.448214			0.0147532
$924$		0			0
$925$	−39.5486	−	12.6355i	−1.30035	−	0.415453i
$926$		0			0
$927$	1.26175	+	1.26175i	0.0414414	+	0.0414414i
$928$		0			0
$929$		−	43.0476i		−	1.41235i	−0.708039	−	0.706173i	$-0.750420\pi$
$929$		−	43.0476i		−	1.41235i	0.708039	−	0.706173i	$-0.249580\pi$
$930$		0			0
$931$	6.17528	+	6.17528i	0.202387	+	0.202387i
$932$		0			0
$933$			20.4524i			0.669580i
$934$		0			0
$935$	1.26391	−	8.10896i	0.0413343	−	0.265192i
$936$		0			0
$937$	−11.1198	−	11.1198i	−0.363268	−	0.363268i	0.501747	−	0.865015i	$-0.332691\pi$
$937$	−11.1198	−	11.1198i	−0.363268	−	0.363268i	−0.865015	+	0.501747i	$0.832691\pi$
$938$		0			0
$939$	−42.1125	−	42.1125i	−1.37429	−	1.37429i
$940$		0			0
$941$	−2.76429	+	2.76429i	−0.0901131	+	0.0901131i	−0.750726	−	0.660613i	$-0.770296\pi$
$941$	−2.76429	+	2.76429i	−0.0901131	+	0.0901131i	0.660613	+	0.750726i	$0.270296\pi$
$942$		0			0
$943$	19.0050	−	19.0050i	0.618889	−	0.618889i
$944$		0			0
$945$	14.2132	+	19.4621i	0.462357	+	0.633101i
$946$		0			0
$947$	−6.77325			−0.220101			−0.110051	−	0.993926i	$-0.535101\pi$
$947$	−6.77325			−0.220101			−0.110051	+	0.993926i	$0.535101\pi$
$948$		0			0
$949$	24.5634	−	24.5634i	0.797360	−	0.797360i
$950$		0			0
$951$	5.73728			0.186044
$952$		0			0
$953$	−28.6073	+	28.6073i	−0.926682	+	0.926682i	−0.997490	−	0.0708083i	$-0.977442\pi$
$953$	−28.6073	+	28.6073i	−0.926682	+	0.926682i	0.0708083	+	0.997490i	$0.477442\pi$
$954$		0			0
$955$	−3.62268	+	23.2423i	−0.117227	+	0.752103i
$956$		0			0
$957$			30.6812i			0.991782i
$958$		0			0
$959$	−13.8156			−0.446129
$960$		0			0
$961$	−42.4158			−1.36825
$962$		0			0
$963$		−	3.97143i		−	0.127978i
$964$		0			0
$965$	−10.5105	−	14.3919i	−0.338344	−	0.463292i
$966$		0			0
$967$	−18.3434	+	18.3434i	−0.589882	+	0.589882i	−0.937600	−	0.347717i	$-0.886957\pi$
$967$	−18.3434	+	18.3434i	−0.589882	+	0.589882i	0.347717	+	0.937600i	$0.386957\pi$
$968$		0			0
$969$	6.89753			0.221581
$970$		0			0
$971$	−9.66321	+	9.66321i	−0.310107	+	0.310107i	−0.844951	−	0.534844i	$-0.820370\pi$
$971$	−9.66321	+	9.66321i	−0.310107	+	0.310107i	0.534844	+	0.844951i	$0.320370\pi$
$972$		0			0
$973$	41.2376			1.32202
$974$		0			0
$975$	9.19481	−	28.7793i	0.294470	−	0.921677i
$976$		0			0
$977$	−40.1076	+	40.1076i	−1.28316	+	1.28316i	−0.344293	+	0.938862i	$0.611881\pi$
$977$	−40.1076	+	40.1076i	−1.28316	+	1.28316i	−0.938862	+	0.344293i	$0.888119\pi$
$978$		0			0
$979$	−42.5895	+	42.5895i	−1.36117	+	1.36117i
$980$		0			0
$981$	−1.98688	−	1.98688i	−0.0634362	−	0.0634362i
$982$		0			0
$983$	−39.6507	−	39.6507i	−1.26466	−	1.26466i	−0.948808	−	0.315854i	$-0.897709\pi$
$983$	−39.6507	−	39.6507i	−1.26466	−	1.26466i	−0.315854	−	0.948808i	$-0.602291\pi$
$984$		0			0
$985$	21.7297	+	3.38692i	0.692367	+	0.107916i
$986$		0			0
$987$			5.52640i			0.175907i
$988$		0			0
$989$	5.04027	+	5.04027i	0.160271	+	0.160271i
$990$		0			0
$991$			5.77959i			0.183595i	0.995778	+	0.0917974i	$0.0292612\pi$
$991$			5.77959i			0.183595i	−0.995778	+	0.0917974i	$0.970739\pi$
$992$		0			0
$993$	−9.43621	−	9.43621i	−0.299449	−	0.299449i
$994$		0			0
$995$	−9.06090	+	58.1327i	−0.287250	+	1.84293i
$996$		0			0
$997$	28.8109			0.912449			0.456225	−	0.889865i	$-0.349201\pi$
$997$	28.8109			0.912449			0.456225	+	0.889865i	$0.349201\pi$
$998$		0			0
$999$			40.8756i			1.29325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.j.d.63.5	yes	32
4.3	odd	2	inner	1280.2.j.d.63.12	yes	32
5.2	odd	4		1280.2.s.c.1087.5	yes	32
8.3	odd	2		1280.2.j.c.63.5	✓	32
8.5	even	2		1280.2.j.c.63.12	yes	32
16.3	odd	4		1280.2.s.c.703.5	yes	32
16.5	even	4		1280.2.s.d.703.5	yes	32
16.11	odd	4		1280.2.s.d.703.12	yes	32
16.13	even	4		1280.2.s.c.703.12	yes	32
20.7	even	4		1280.2.s.c.1087.12	yes	32
40.27	even	4		1280.2.s.d.1087.5	yes	32
40.37	odd	4		1280.2.s.d.1087.12	yes	32
80.27	even	4		1280.2.j.c.447.5	yes	32
80.37	odd	4		1280.2.j.c.447.12	yes	32
80.67	even	4	inner	1280.2.j.d.447.12	yes	32
80.77	odd	4	inner	1280.2.j.d.447.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1280.2.j.c.63.5	✓	32	8.3	odd	2
1280.2.j.c.63.12	yes	32	8.5	even	2
1280.2.j.c.447.5	yes	32	80.27	even	4
1280.2.j.c.447.12	yes	32	80.37	odd	4
1280.2.j.d.63.5	yes	32	1.1	even	1	trivial
1280.2.j.d.63.12	yes	32	4.3	odd	2	inner
1280.2.j.d.447.5	yes	32	80.77	odd	4	inner
1280.2.j.d.447.12	yes	32	80.67	even	4	inner
1280.2.s.c.703.5	yes	32	16.3	odd	4
1280.2.s.c.703.12	yes	32	16.13	even	4
1280.2.s.c.1087.5	yes	32	5.2	odd	4
1280.2.s.c.1087.12	yes	32	20.7	even	4
1280.2.s.d.703.5	yes	32	16.5	even	4
1280.2.s.d.703.12	yes	32	16.11	odd	4
1280.2.s.d.1087.5	yes	32	40.27	even	4
1280.2.s.d.1087.12	yes	32	40.37	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.81199i q^{3} +(-2.20939 - 0.344369i) q^{5} +(1.54814 - 1.54814i) q^{7} -0.283291 q^{9} +(2.69839 - 2.69839i) q^{11} +3.33474 q^{13} +(-0.623991 + 4.00338i) q^{15} +(-0.680078 + 0.680078i) q^{17} +(2.79866 - 2.79866i) q^{19} +(-2.80521 - 2.80521i) q^{21} +(1.75563 + 1.75563i) q^{23} +(4.76282 + 1.52169i) q^{25} -4.92264i q^{27} +(-3.13750 - 3.13750i) q^{29} +8.56830i q^{31} +(-4.88944 - 4.88944i) q^{33} +(-3.95358 + 2.88732i) q^{35} -8.30361 q^{37} -6.04250i q^{39} -10.8252i q^{41} +2.87092 q^{43} +(0.625900 + 0.0975564i) q^{45} +(-0.985023 - 0.985023i) q^{47} +2.20651i q^{49} +(1.23229 + 1.23229i) q^{51} -13.1354i q^{53} +(-6.89103 + 5.03255i) q^{55} +(-5.07113 - 5.07113i) q^{57} +(4.36188 + 4.36188i) q^{59} +(-7.83616 + 7.83616i) q^{61} +(-0.438574 + 0.438574i) q^{63} +(-7.36775 - 1.14838i) q^{65} -13.0450 q^{67} +(3.18118 - 3.18118i) q^{69} +0.134408 q^{71} +(7.36590 - 7.36590i) q^{73} +(2.75728 - 8.63016i) q^{75} -8.35497i q^{77} +7.88100 q^{79} -9.76962 q^{81} -12.0979i q^{83} +(1.73676 - 1.26836i) q^{85} +(-5.68510 + 5.68510i) q^{87} -15.7833 q^{89} +(5.16265 - 5.16265i) q^{91} +15.5256 q^{93} +(-7.14711 + 5.21957i) q^{95} +(-3.00550 + 3.00550i) q^{97} +(-0.764428 + 0.764428i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{9} + 16 q^{13} + 8 q^{17} + 8 q^{21} + 16 q^{25} - 16 q^{29} + 56 q^{33} - 40 q^{45} - 8 q^{57} - 8 q^{61} - 72 q^{65} + 40 q^{69} + 8 q^{73} - 64 q^{81} - 24 q^{85} - 16 q^{89} + 224 q^{93}+ \cdots + 72 q^{97}+O(q^{100}) \) 32 * q - 32 * q^9 + 16 * q^13 + 8 * q^17 + 8 * q^21 + 16 * q^25 - 16 * q^29 + 56 * q^33 - 40 * q^45 - 8 * q^57 - 8 * q^61 - 72 * q^65 + 40 * q^69 + 8 * q^73 - 64 * q^81 - 24 * q^85 - 16 * q^89 + 224 * q^93 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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